Analysis of Doppler-Broadened X-ray Emission
Line Profiles from Hot Stars
David Cohen - Swarthmore College
with
Roban Kramer - Swarthmore College
Stanley Owocki - Bartol Research Institute
Outline
0. The astrophysical context
I.
Introduction: What line profiles can tell us
II. The basic model
III. Fitting Chandra data from hot stars - z Pup:
Constraining parameters
IV. What the data are telling us: Integration with
other X-ray spectral diagnostics
What produces hot-star X-rays?
Hot stars are thought
not to have convective
envelopes, magnetic
activity, or coronae
Hot stars have massive radiationdriven winds, with a significant
amount of continuum opacity
What Line Profiles Can Tell Us
The wavelength of an emitted photon is proportional to the
line-of-sight velocity:
Line shape maps emission measure at each velocity/wavelength
interval
Continuum absorption by the cold stellar wind affects the
line shape
Correlation between line-of-sight velocity and absorption optical
depth will cause asymmetries in emission lines
X-ray line profiles can provide the most direct observational
constraints on the X-ray production mechanism in hot stars
Emission Profiles from a Spherically
Symmetric, Expanding Medium
A uniform shell
gives a rectangular
profile.
A spherically-symmetric, X-ray emitting
wind can be built up from a series of
concentric shells.
Occultation by the star
removes red photons,
making the profile
asymmetric
Continuum Absorption Acts Like Occultation
Red photons are preferentially absorbed, making the line
asymmetric: The peak is shifted to the blue, and the red wing
becomes much less steep.
We calculate line profiles using a 4-parameter model
3 parameters describe the spatial and velocity distribution of the
emission:
Ro is the minimum radius of X-ray emission;
b describes the acceleration of the wind;
q parameterizes the radial dependence of the filling factor.
1 parameter, t*, describes the level of continuum absorption in the
overlying wind.
A wind terminal velocity is assumed based on UV
observations, and the calculated line profile is convolved with
the appropriate instrument-response function for each line.
In addition to the
wind-shock model,
our empirical line profile model can also describe a corona
With most of the
emission
concentrated near
the photosphere
and with very little
acceleration, the
coronal line
profiles are very
narrow.
A wide variety of windshock characteristics can
be modeled
Line profiles
change in
characteristic ways
with t* and Ro,
becoming broader
and more skewed
with increasing t*
and broader and
more flat-topped
with increasing Ro.
t=1,2,8
Ro=1.5
Ro=3
Ro=10
The X-ray lines in O stars are observed to be broad;
z Pup is the prototypical O supergiant with a strong wind
Ne X
Fe XVII
O VIII
N VII
We fit six lines in the Chandra MEG spectrum of z Pup
For each line, we are able to achieve a good fit with
reasonable model parameters
blend
Best-fit model: t=1.0, Ro=1.4, q=-0.4, with b=1 fixed
We also determine the extent of the confidence limits within the model parameter
space – Note how the line profile changes with increasing wind opacity
68%
95%
99%
The fitted lines span a range of wind optical
depth and X-ray temperature
The Fe XVII line at 15 Å (left) has a more typical profile, while the
N VII (right) is more flat-topped and broad. And despite having a
longer wavelength, it doesn’t suffer a lot of attenuation.
The confidence regions define the widest possible
variation among acceptable models
highest t
best fit
model
lowest t
The best fit and two other acceptable (at the 95% confidence level) fits
The best-fit parameters and 95% confidence limits are
derived for all six lines
The formation radii for all lines are close to the
surface of the star
 very little radial dependence of the
X-ray filling factor
Wind optical depth is only moderate, and
 only varies weakly with wavelength
Discussion
• A spherically symmetric, distributed wind X-ray source (i.e.
‘wind shock model’) can account for the line profiles in z Pup
in a reasonable way
• The X-ray formation zone begins close to the photosphere
(within 3 R for all lines)
• Continuum absorption by the overlying cool wind is
important, but not as strong as models (and UV observations of
the wind) would seem to suggest (t is between 8 and 20 according to
models calculated by Hillier et al. (1993)).
more Discussion…
• Above Ro, the amount of X-ray emitting gas scales close to
density-squared (i.e. the filling factor has very little radial
dependence)
• The lower-than-expected absorption could have to do with
overestimation of the wind opacity, or possibly with
overestimation of the mass-loss rate…but, it could also be
due to clumping in the wind (which might also be associated
with the wind-shock process itself)
• Other O stars observed with Chandra do not seem to have
wind absorption signatures (broad but symmetric lines) and B
stars have basically narrow lines – could this have to do with
clumping too? Or non-spherical winds? (see Owocki’s poster
on MHD simulations of magnetic hot star winds)
Extra Slides
Rad-hydro simulations of the lineforce instability – copius shockheated material distributed
throughout the wind
The Basic Model
Described in Owocki & Cohen (2001, ApJ, 559, 1108), the model assumes a smoothly and spherically
symmetrically distributed accelerating X-ray emitting plasma subject to continuum attenuation by the
cold stellar wind.
L  8
1

1

d  r  (, r)e
2
t , r
R
v(r )  v (1  R* / r )
The wind velocity is assumed to
have the form:
The optical depth of the wind
along a ray with impact
parameter p is given by:
2

t  p, z   t  z
b
R dz'
b
r' 2 1  R r' 
Note that while spherical symmetry is natural for the emission,
cylindrical symmetry is natural for the absorption; Combining
expressions in these two sets of variables requires the transformation:
(r) ~    o 1  v cf (r) ~   r q
The delta function picks out the
resonance velocity, mapping  into .
dr
which dictates the density of
the wind as well.
where
r' 
M
t 
4v R
p  z'
2
2
for r  Ro
q parameterizes the radial
fall-off of the emissivity.
Ro parameterizes
the lower radius
of X-ray
emission